Let be a triangle with sides . Let be its incentre and let the incircle touch the sides on respectively. Then we have (from showing congruences): . Refer to the image.
So, we have that for some .
Refer to the image.
Now, in and
Hence, from the RHS rule of congruency these two are congruent.
and are congruent , giving
Similarly we have &
Solutions to these problems are welcome.